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Proceedings of the London Mathematical Society (1)

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Applications of Atiyah–Hirzebruch spectral sequences for motivic cobordism
Nobuaki Yagita
Journal:

Proceedings of the London Mathematical Society / Volume 90 / Issue 3 / May 2005

Published online by Cambridge University Press:

22 April 2005, pp. 783-816

Print publication:

May 2005
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In this paper, we study applications of Atiyah–Hirzebruch spectral sequences for motivic cobordism recently found by Hopkins and Morel. For example, we compute the mod 2 motivic cohomology of a reduced Cech complex of a splitting variety according to Orlov, Vishik and Voevodsky. The cobordism ring $MGL / 2^{*,*} (Spec(\mathbb{R}))$ is computed and compared with the results of the real cobordism theory of Hu and Kriz. Moreover, we study algebraic cobordism of the classifying spaces $BG$ for algebraic groups over $\mathbb{C}$. For example, the Chow ring $CH^* (BG_2)_(2)$ for the exceptional Lie group $G_2$ is determined by using motivic cobordism and motivic cohomology.